1. Field of the Invention
This invention relates to sensors. Particularly, this invention relates to sensor techniques for tomographic imaging.
2. Description of the Related Art
Imaging of samples through projections has been an important concept ever since the discovery of x-rays, and has been used in the gravitational theory and radio astronomy before becoming widespread through computerized tomography in x-ray, electron, and optical imaging, among others. See e.g., A. Cormack, J. Appl. Phys. 34, 2722 (1963); G. Hounsfield, British J. Radiol. 46, 1016 (1973); D. J. de Rosier arid A. Klug, Nature (London) 217 130 (1968); and D. E. Kuhl and R. Q. Edwards, Radiol. 80, 653 (1963). The first report of magnetic resonance imaging (MRI) had its roots in image reconstruction from projections. See, P. C. Lauterbur, Nature (London) 242, 190 (1973). Computerized tomographic image reconstruction algorithms for conventional radiation-based tomography are by now well developed and can be easily transferred to novel imaging methodologies such as the one described in this disclosure on stripe sensor tomography. See e.g, G. T. Herman, Image Reconstruction from Projections, Academic Press, New York (1980); F. Natterer, The Mathematics of Computerized Tomography, John Wiley & Sons, New York (1986); A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging SIAM, Philadelphia (2001); S. R. Deans, Tile Radon Transform and Some of Its Applications, Krieger Publishing Company, Malabar (1993); and P. T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Oxford University Press. New York (1991), which are incorporated by reference herein.
The various disciplines of scanning probe microscopy conventionally employ a point-by-point raster scanning of the sample in the x-y plane as a common way of obtaining a two-dimensional image of the sample. However, it can frequently be the case that the scanning sensor is not of the point type, but is instead of the stripe shape, typically due to the thin-film lithographic character of sensor fabrication. For example, in scanning magneto-resistance microscopy the imaging sensor is a thin film magneto-resistive element of small thickness, t, and much larger width, w. See, S Y. Yamamoto and S. Schultz. Appl. Phys. Lett. 69, 3263 (1996). By raster scanning of this sensor in the x-y plane, a two-dimensional image of a magnetic sample can be obtained. See also, S. Y. Yamamoto, R. O'Barr, S. Schultz, and A. Scherer, IEEE Trans. Magn. 33, 1016 (1997); M. Todorovic, S. Schultz, J. Wong, and A. Scherer, Appl. Phys. Lett. 74, 2516 (1999); and M. Barbic, S. Schultz, J. Wong, and A. Scherer, IEEE Trans. Magn. 37, 1657 (2001). There has been a perceived notion in such reports that two-dimensional images obtained with a stripe-type magneto-resistive sensor are limited in spatial resolution by thickness, t, in the x-direction, and width, w, in the y-direction.
In view of the foregoing, there is a need in the art for apparatuses and methods for more efficient apparatuses and methods for tomographic imaging, e.g. using stripe-like sensors. In addition, there is a need for such apparatuses and methods that can deliver high spatial resolution with reduced scanning requirements. There is further a need for such imaging apparatuses and methods that can operate more quickly and efficiently than conventional techniques. These and other needs are met by the present invention as detailed hereafter.